Perturbative Approach for the Analysis of Charge Distribution on Arbitrarily Shaped Conductors

Mauro Bologna,Bernardo Tellini,Kristopher J Chandia,Gianluca Caposciutti

doi:10.1109/access.2021.3116193

Mauro Bologna, Bernardo Tellini + Show 2 more

Open Access

https://doi.org/10.1109/access.2021.3116193

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Journal: IEEE Access	Publication Date: Jan 1, 2021
License type: CC BY 4.0

Affiliation: University of Pisa, University of Tarapacá

Abstract

In this paper, we analyze the electrostatic charge distribution on arbitrarily shaped conductor surfaces. Following a perturbative approach, we derive an approximate analytical formulation of the problem. We start from the known case of a conducting ellipsoid, we adopt a deformed ellipsoidal coordinate system, and we search for the zero-order approximated solution of the problem. We also focus on arbitrary-shaped thin foils, showing that the charge density is divergent on their borders. We then define the applicability range of the proposed approach expressing the contour equation as the Fourier series. Finally, we present a detailed error analysis for several polygonal contours, comparing the analytical results with those obtained via a numerical analysis based on the Finite Element Methods (FEM).

Highlights

The problem of finding the electrostatic charge distribution on a charged conductor is a fascinating problem that many classical electrodynamics textbooks solve in several analytical cases [1]–[3]
ELECTRICAL POTENTIAL GENERATED BY A CONDUCTOR SURFACE Our goal is to find an analytical solution of
In this paper, we presented an analytical formulation of the problem of electrostatic charge distributions on arbitrarily shaped conductor surfaces

Summary

Introduction

The problem of finding the electrostatic charge distribution on a charged conductor is a fascinating problem that many classical electrodynamics textbooks solve in several analytical cases [1]–[3]. Several practical problems are related to the identification of the charge distribution and possibly its optimization, on thin surface domains, for instance, in energy harvesting and designing devices [10], [11], semiconductors [12], photovoltaics, and optoelectronics [13], [14]. In electrical accumulators, such as lithium batteries, the study of the charge density distribution has a crucial role in developing new techniques to reduce dendrite growth [15], [16]. The knowledge of the charge distribution of a generic geometry of the conductor can allow for a better designing the conductor geometries and for reducing the possibility of occurrence of electrostatic discharge [17]–[19]

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